The question is: Find the Inflection Point(s) and Intervals of concavity for the curve
Equation of Curve: 1/x - 1/(x-1)
The Attempt at a Solution
Ok so to find the Inflection point, we have been taught to find the second derivative of the equation, equate it to zero then solve for x. Ok so I tried this and I just can't seem to solve for X, the equation becomes enormous and unruly and I just don't know how to solve it. Anyways, I was looking at the graph and I couldn't see anywhere that would be an inflection point. So my question is, is there even any inflection points on this graph, and if the answer is no, then does that mean that there are no intervals of concavity as well?
Edit: Scratch what I said about no concavity, I think just by looking at the graph that it is Concave down when: x<0, x>1 and it it Concave up when: 0<x<1. However, my question about there being no inflection point still stands.
Thanks in advance =D